Due to the rapid progress of miniaturization techniques of electronics devices, various mobile electronic devices are spreading. Recently, batteries are used as a power source for vehicles such as automobiles. Therefore, batteries exhibiting a long lifetime, high safety, and excellent input-and-output characteristics are required.
Batteries including, as a negative electrode active material, a lithium-titanium composite oxide exhibit excellent safety and a long lifetime. The lithium titanium composite oxide, however, is an insulator in a low state-of-charge, and thus batteries including such a negative electrode active material have a problem that the input-and-output characteristics are low in a low state-of-charge.